The former Manchester United striker was interviewed by Villa owner Randy Lerner over the weekend.
But Solskjaer has opted not to be considered as Alex McLeish's successor for personal reasons.
Solskjaer was the favourite with the bookmakers to take charge of Villa who only just avoided relegation from the Premier League.
But sources close to the club are keen to stress Solskjaer was never offered the job by Lerner.
Lerner and chief executive Paul Faulkner will now step up their bid in other directions to replace McLeish who was sacked nine days ago.
Brendan Rodgers (Swansea), Paul Lambert (Norwich) and Roberto Martinez (Wigan) are potential candidates.
Rodgers and Lambert impressed with their respective clubs during their first season in the Premier League although it is understood Villa have yet to approach either club.
Martinez turned down the chance to take charge at Villa last summer after Gerard Houllier was forced to quit on health grounds.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.